L-U factorization procedure [11]. The change vector is
k
then added to the previous iterate x to obtain the new

iterate:

k+l k
x0 = x + Ax

When Ax is sufficiently small, the iteration is terminated.

In order to apply Newton's method to the steady-state

determination, the partial derivatives which make up the

Jacobian matrix must be determined. The adjoint network

concept may be employed to calculate these partial

derivatives efficiently. Once again, capacitors and
inductors are modeled as shown in Fig. 2-3. Upon appli-
cation of Tellegen's theorem to the original networkIZ
and its mutually reciprocal adjoint network Z--as shown
in Fig. 2-4--we may write

t +T
/tT [vB(t)B)(T) iB(t)B(T)] dt = 0 (2.64)
t0 B

where vB and i are the Bth branch voltage and current in
the original networkZ, ,B' and )B are the Bth branch
voltage and current in the adjoin'- network't, and the
indicated summation is over all network branches. Upon an
incremental change in the parameters of the original network,
(2.64) becomes